What is the current value of the scale factor?

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Discussion Overview

The discussion centers on the current value of the scale factor in cosmology, particularly its normalization and implications for understanding the universe's expansion. Participants explore theoretical aspects and definitions related to the scale factor, including its relationship with the Hubble constant.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the current value of the scale factor, noting the known value of the Hubble constant and its relationship to the scale factor.
  • Another participant states that the scale factor is typically normalized to a value of a(t_0)=1 at the present time, referencing an external thread for further context.
  • A different participant reiterates the normalization of the scale factor and asks for a specific numerical value for R₀.
  • One participant asserts that R₀ is defined as 1, emphasizing that this is a dimensionless number and that the choice of R at a single time does not affect the underlying physics.
  • Another participant agrees that the scale factor is traditionally set to unity at the current time and discusses how this normalization allows for calculations regarding the universe's past state.
  • A participant questions the necessity of defining a=R/R₀ when R₀ is set to 1, suggesting that it may simply be a matter of nomenclature.

Areas of Agreement / Disagreement

Participants generally agree that the scale factor is normalized to 1 at the present time, but there is some debate regarding the implications of this normalization and the necessity of the definition involving R₀.

Contextual Notes

The discussion includes assumptions about the normalization of the scale factor and its implications for cosmological models, which may not be universally accepted or understood.

I_wonder
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Do cosmologists know what is the current value of the scale factor? I know we have a current value for the Hubble constant H, and I know H=a'/a. But what about the value of a?

Thanks!
 
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cristo said:
Usually, the scale factor is normalised so that it takes the value a(t_0)=1 at present times. See this thread https://www.physicsforums.com/showthread.php?t=222284, for example.

What is the current value of the scale factor(R₀)?

a= R(t)/R₀

Give me the number.

Thanks
 
R0= 1, which is a dimensionless number. Why? Because I define it as 1. I can define it as any present number I want to, and it will not change the physics. I can arbitrarily define R at one time only; the value at all other times will scale with my choice of R at the single time I selected.
 
Last edited:
Yeah, the scale factor is traditionally set to unity at the current time. In other words, a(t=2011 A.D.) = 1. Then you can apply the cosmology of your choice (e.g. flat universe with cosmological constant) and answer questions such as how old was the universe when things were 1000 times closer together: a(time in past) / a (now) = 1 / 1000 and solve for the time in the past.
 
BillSaltLake said:
R0= 1, which is a dimensionless number. Why? Because I define it as 1. I can define it as any present number I want to, and it will not change the physics. I can arbitrarily define R at one time only; the value at all other times will scale with my choice of R at the single time I selected.

Thanks, but here appears another question. So why do we define a=R/R0 at all, when R0=1? It means a(t)=R(t), and it is just changing names, isn't it?!
 

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